I have bought flight tickets with my wife and our baby 5 months old, but I can not make it to flight.
Will there be any problems if only my wife with an infant will fly without me, the baby is registered on my seat.
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Call the airline. It's typically not a major problem, but this will be a lot easier if you do some paperwork up front: They should split the reservation into two separate ones, move the baby to your wife's reservation and cancel yours.
This way there is a single reservation for your wife and child that will be flown as booked.